Pat the chicken breasts dry, then season both sides generously with salt, pepper, and a pinch of cinnamon.
Heat the skillet over medium heat and add a tablespoon of olive oil. Once hot, carefully place the chicken breasts in the pan and sear for 5-6 minutes on each side until golden brown.
Remove the chicken from the skillet and set aside on a plate. In the same pan, add the remaining tablespoon of oil and toss in the minced garlic. Sauté for about 30 seconds until fragrant.
Add the diced butternut squash to the skillet and cook for 8-10 minutes, stirring occasionally, until it begins to soften and develops light caramelization.
Stir in the sliced apples, chopped thyme, and a pinch more cinnamon. Cook for another 4-5 minutes until the apples are slightly tender but still holding their shape.
Place the browned chicken breasts back into the skillet among the vegetables. Pour in the chicken broth and bring to a gentle simmer.
Cover the skillet with a lid or foil and cook for 15-20 minutes, until the chicken is cooked through and the squash is tender, with the sauce slightly thickened.
Remove the skillet from heat, check seasoning, and adjust with salt and pepper as needed. Let the dish rest for a couple of minutes so flavors meld.
Jane the skillet gently and serve the chicken and vegetables warm, spooning the flavorful pan juices over each portion.